{"status": "success", "data": {"description_md": "Two externally tangent circles $\\omega_1$ and $\\omega_2$ have centers $O_1$ and $O_2$, respectively. A third circle $\\Omega$ passing through $O_1$ and $O_2$ intersects $\\omega_1$ at $B$ and $C$ and $\\omega_2$ at $A$ and $D$, as shown. Suppose that $AB = 2$, $O_1O_2 = 15$, $CD = 16$, and $ABO_1CDO_2$ is a convex hexagon. Find the area of this hexagon.<br>$\\includegraphics[width=237, height=171, totalheight=171]{https://latex.artofproblemsolving.com/7/4/a/74a9883958ea503b78cb2c07bc71aefe4d830ce9.png}$\n___\nLeading zeroes must be inputted, so if your answer is `34`, then input `034`. Full credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>Two externally tangent circles <span class=\"katex--inline\">\\omega_1</span> and <span class=\"katex--inline\">\\omega_2</span> have centers <span class=\"katex--inline\">O_1</span> and <span class=\"katex--inline\">O_2</span>, respectively. A third circle <span class=\"katex--inline\">\\Omega</span> passing through <span class=\"katex--inline\">O_1</span> and <span class=\"katex--inline\">O_2</span> intersects <span class=\"katex--inline\">\\omega_1</span> at <span class=\"katex--inline\">B</span> and <span class=\"katex--inline\">C</span> and <span class=\"katex--inline\">\\omega_2</span> at <span class=\"katex--inline\">A</span> and <span class=\"katex--inline\">D</span>, as shown. Suppose that <span class=\"katex--inline\">AB = 2</span>, <span class=\"katex--inline\">O_1O_2 = 15</span>, <span class=\"katex--inline\">CD = 16</span>, and <span class=\"katex--inline\">ABO_1CDO_2</span> is a convex hexagon. Find the area of this hexagon.<br/><img src=\"https://latex.artofproblemsolving.com/7/4/a/74a9883958ea503b78cb2c07bc71aefe4d830ce9.png\" width=\"237\" height=\"171\" class=\"problem-image\"/></p>&#10;<hr><p>Leading zeroes must be inputted, so if your answer is <code>34</code>, then input <code>034</code>. Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 6, "problem_name": "2022 AIME II Problem 15", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/22_aime_II_p14"}}